In facilitated diffusion, the carrier protein facilitate the molecule by changing its shape and move the molecule across the membrane. Since that facilitated diffusion is a passivetransport, it does not require ATP.BUT, how can the shape of the carrier protein changes since that it does not have any energy to support?

If two conformations of a protein have similar energies and the energy barrier between the conformations is low enough, random thermal motions can convert the protein between the two conformations. Proteins are constantly being bombarded by solvent, so there is energy in the system that can cause motion; the key is whether the transition energy required to go from one conformation to the other is low enough.

Wiggling is free at room temperature. Moving past a difficult energy barrier can be expensive, a little thermal wiggle isn't enough, you need some significant force. If the energy barrier is low enough, a little thermal wiggle might be sufficient. You've encountered levers (perhaps electrical switches) that contain a spring so that the lever can be on one end-position or the other (say, left or right) but you must push against the spring to move the lever past the middle position before is snaps into the other state with assistance from the spring. This is an analogy for a protein that has a significant transition energy. If the spring breaks, the switch can freely flop between the two states, like a protein with a low transition energy barrier.

If the energy barrier between protein conformations is low, a protein can randomly pick up cargo on one side of the membrane and (THWACK with a solvent molecule) change conformation to release the cargo on the other side. Occasionally a cargo molecule will be moved in the "wrong way", against its gradient, but on average more cargo will dock at the high-concentration side than at the low-concentration side so the overall facilitated diffusion will be down the concentration gradient.